The stress field due to an interfacial edge dislocation in a multi-layered medium

Khanna, Aditya; Kotousov, Andrei

doi:10.1016/j.ijsolstr.2015.06.030

Cited by 7 publications

(2 citation statements)

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“…Extensions of the formalism to modern free vibration problems as well as buckling [61] and bending [62] analysis of metallic multilayered structures are also possible. For instance, the time-harmonic interactions between semicoherent heterophase interfaces with core-spreading dislocation structures [63] with extrinsic dislocation loops [64] and interfacial cracks [65,66] in multifunctional composites would be of great importance to understand their effects on the natural frequencies and lower and higher thermoelastic mode shapes for future renewable energy devices in aerospace structures [67]. Due to the present versatile formalism to take care of imperfect interfaces, other interfacial considerations as the elastic-slip interface model [68,69] and surface/interface model [70] raised by Gurtin and Murdoch [71] can be introduced for appropriate applications, as well as nonlocal size effects [13] in nano-and micro-scale structures.…”

Section: Discussionmentioning

confidence: 99%

Free vibration of fully coupled thermoelastic multilayered composites with imperfect interfaces

Vattré

Pan

Chiaruttini

2021

Composite Structures

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A fully coupled thermoelastic framework is formulated to cope with the free vibration response of anisotropic multilayered plates in three dimensions. The laminated structure consists of homogeneous laminae of arbitrary thickness and width under simply supported edge conditions in thermal environment. The general and exact field expressions of the temperature, heat flux, displacement and stress components are expressed in terms of double Fourier series expansions in any rectangular plate, which lead to the extended Stroh formalism with thermomechanical coupling effects in a concise and compact matrix form. Different imperfect interface conditions are introduced to characterize specific structural and thermal contact properties at the bounding interfaces, and further to determine the finite complex valued coefficients in the suitable series relations. The complete time-harmonic solutions in the laminated composites in the presence of perfect/imperfect interfaces are recursively obtained by means of the modified dual variable and position technique with explicit layer-to-layer transfer matrices. Results are obtained for different layups, length-to-thickness ratios and interfacial boundary conditions for two application examples, namely the graphite/epoxy cross-ply composites and the thermal barrier coatings on superalloys, without suffering from numerical exponential instability. These investigations reveal that the natural frequencies and first and higher vibration mode shapes of the multilayered structures can be considerably affected by increasing the environmental temperature and the severity of the interfacial imperfections. Since the through-thickness stress distribution in 2, 5, and 10 layered composites appears to be strongly correlated to the layups, such modal stress analysis could be exploited to locate the fatigue hotspots operated in dynamic structures and to guide the structural design of aircraft and spacecraft composite laminates subjected to residual vibrations.

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Section: Discussionmentioning

confidence: 99%

Free vibration of fully coupled thermoelastic multilayered composites with imperfect interfaces

Vattré

Pan

Chiaruttini

2021

Composite Structures

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“…Wu and Chid (1995) derived the line-dislocation solution in an anisotropic strip; Kelly et al (1995) solved the stress field due to a line dislocation in layered isotropic media; Ma and Lee (2009) presented a theoretical analysis for dislocations in an anisotropic and magnetoelectroelastic layered half-plane where the purely elastic solution is a special case of their solution. More recent contributions on line dislocation-induced fields in layered elastic media are by Kuo (2014), Khanna and Kotousov (2015) and Xia et al (2016). In geophysics where the source is 2D fault, we refer to the works by Freund and Barnett (1976), Rybicki (1971Rybicki ( , 1986 and Savage (1980Savage ( , 1998.…”

Section: General Solutions In Elastic or Viscoelastic Layered Half-sp...mentioning

confidence: 99%

Green’s functions for geophysics: a review

Pan

2019

Rep. Prog. Phys.

118

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The Green's function (GF) method, which makes use of GFs, is an important and elegant tool for solving a given boundary-value problem for the differential equation from a real engineering or physical field. Under a concentrated source, the solution of a differential equation is called a GF, which is singular at the source location, yet is very fundamental and powerful. When looking at the GFs from different physical and/or engineering fields, i.e. assigning the involved functions to real physical/engineering quantities, the GFs can be scaled and applied to large-scale problems such as those involved in Earth sciences as well as to nano-scale problems associated with quantum nanostructures. GFs are ubiquitous and everywhere: they can describe heat, water pressure, fluid flow potential, electromagnetic (EM) and gravitational potentials, and the surface tension of soap film. In the undergraduate courses Mechanics of Solids and Structural Analysis, a GF is the simple influence line or singular function. Dropping a pebble in the pond, it is the circular ripple traveling on and on. It is the wave generated by a moving ship in the opening ocean or the atom vibrating on a nanoscale sheet induced by the atomic force microscopy. In Earth science, while various GFs have been derived, a comprehensive review is missing. Thus, this article provides a relatively complete review on GFs for geophysics. In section 1, the George Green's potential functions, GF definition, as well as related theorems and basic relations are briefly presented. In section 2, the boundary-value problems for elastic and viscoelastic materials are provided. Section 3 is on the GFs in full-and half-spaces (planes). The GFs of concentrated forces and dislocations in horizontally layered half-spaces (planes) are derived in section 4 in terms of both Cartesian and cylindrical systems of vector functions. The corresponding GFs in a self-gravitating and layered spherical Earth are presented in section 5 in terms of the spherical system of vector functions. The singularity and infinity associated with GFs in layered systems are analyzed in section 6 along with a brief review of various layer matrix methods. Various associated mathematical preliminaries are listed in appendix, along with the three sets of vector function systems. It should be further emphasized that, while this review is targeted at geophysics, most of the GFs and solution methods can be equally applied to other engineering and science fields. Actually, many GFs and solutions methods reviewed in this article are derived by engineers and scientists from allied fields besides geophysics. As such, the updated approaches of constructing and deriving the GFs reviewed here should be very beneficial to any reader.

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Analysis of 3D Problems of Dynamic Loading of Elastic Piecewise-Homogeneous Bodies with Internal Cracks

Stankevych

2023

J Math Sci

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The stress field due to an interfacial edge dislocation in a multi-layered medium

Cited by 7 publications

References 40 publications

Free vibration of fully coupled thermoelastic multilayered composites with imperfect interfaces

Free vibration of fully coupled thermoelastic multilayered composites with imperfect interfaces

Green’s functions for geophysics: a review

Analysis of 3D Problems of Dynamic Loading of Elastic Piecewise-Homogeneous Bodies with Internal Cracks

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